Performance Measurement for Option Portfolios in a Stochastic Volatility Framework
41 Pages Posted: 7 Feb 2018
Date Written: January 29, 2018
Measuring the performance of stock portfolios that include options is challenging due to options’ nonlinearity in the underlying and their exposure to volatility risk. Our contribution to the literature is twofold: First, we provide a theoretically rigorous derivation of the time-variable factor loadings in a multi-factor model under stochastic volatility according to Heston (1993) when an option factor is included. We show that (i) any option factor is suitable if discrete returns are considered in instantaneous time and that (ii) the option factor’s loading equals the fraction of the volatility elasticities of the portfolio and of the option factor while the option factor’s underlying elasticity enters the factor loading of the underlying. Second, in applications however, time has to be discretized and factor loadings are usually estimated in a single regression over a certain time horizon, which regularly leads to a bias in performance measurement. We run a simulation analysis to analyze the size of this bias when diﬀerent option factors from the common literature are used and propose a two-step procedure to keep the bias small.
Keywords: Performance Measurement, Option Portfolios, Stochastic Volatility, Heston, Nonlinearity, Volatility Risk, Option-Based Factors, Discrete Returns, Continuous Returns
JEL Classification: C13, C60, C61, C62, G10, G12
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